The E3CI components are defined as follows:
i) HEAT STRESS
BASELINE
CALCULATION: On the reference period 1981-2010, for each calendar day, the
maximum temperature of the surrounding five days is considered. The 95th percentile among the 150 values (5 days x 30 years) is computed and assumed as threshold. For each month j, the
mean value \mu\left(j,\ T_{max}\right)\ and the
standard deviation \sigma\left(j,\ T_{max}\right)\ of the
number of days exceeding the corresponding threshold are calculated.
STANDARDIZED
ANOMALY COMPUTATION: Each month j and year k the number of days exceeding the corresponding threshold {HS}_{j,k} is standardized according to the formula:
{HS}_{std,j,k}=\frac{{HS}_{j,k}-\mu\left(j,\ T_{max}\right)}{\sigma\left(j,\ T_{max}\right)}
ii) COLD STRESS
BASELINE CALCULATION: On the reference period 1981-2010, for each
calendar day, the minimum temperature of the surrounding five days is
considered. The 5th percentile among the 150 values (5 days x 30
years) is computed and assumed as threshold. For each month j, the mean value \mu\left(j,\ T_{min}\right)\ and the standard deviation \sigma\left(j,\ T_{min}\right)\ of the number of days lower than the corresponding threshold are
calculated.
STANDARDIZED ANOMALY COMPUTATION: Each month j and year k the number of days lower than the corresponding threshold {CS}_{j,k} is standardized according to the formula:
{CS}_{std,j,k}=\frac{{CS}_{j,k}-\mu\left(j,\ T_{min}\right)}{\sigma\left(j,\ T_{min}\right)}
iii) DROUGHT
BASELINE CALCULATION: Standard Precipitation Index (SPI) is assumed as reference
indicator considering 3 months as accumulation period of interest (SPI-3). Over
1981-2010, for each month j the 30 cumulated values are fitted to a gamma probability distribution which is then transformed into a normal distribution.
STANDARDIZED ANOMALY COMPUTATION: For each month j and year {SPI-3}_{j,k} value represents units of standard deviation
from the long-term reference mean. According to the canonical approach, positive
SPI indicate values greater than median precipitation and negative values
indicate less than median precipitation. In E3CI, to maintain the
consistency with the other components, the opposite of {SPI-3}_{j,k} is taken.
iv) EXTREME PRECIPITATION
BASELINE CALCULATION: On the reference period 1981-2010, for each month j, the 95th percentile of daily precipitation is computed. Then, the exceedance value at
monthly basis is computed as:
{EP}_{j,k}=\sum_{i=1}^{n_j}{\max{\left[0;\ P_{i,j,k}-P_{95,j}\right]}\ }
where P_{i,j,k} represents the daily precipitation (day i, month j, year k
Over the reference period, for each month j, the mean value \mu\left(\ {EP}_j\right)\ and the standard deviation \sigma\left(\ {EP}_j\right)\ of the exceedance value are calculated.
STANDARDIZED ANOMALY COMPUTATION: Each month j and year k the exceedance value is standardized according to the formula:
{EP}_{std,j,k}=\frac{{EP}_{j,k}-\mu\left({EP}_j\right)}{\sigma\left(\ {EP}_j\right)}
v) EXTREME WIND
BASELINE CALCULATION: On the reference period 1981-2010, for each month j, the 95th percentile of daily maximum wind speed is computed, w_{95,j}. Then, at monthly basis, Local Loss Index (LLI, Donat et al., 2011; doi:10.5194/nhess-11-1351-2011) is calculated as:
{LLI}_{j,k}=\sum_{i=1}^{n_j}max\left[0;\left(\frac{w_{max,i,j,k}}{w_{95,j}}-1\right)^3\right]
Where w_{max,i,j,k} is the maximum wind speed computed considering mean hourly values. Over the reference period, for each month j, the mean value \mu\left(\ {LLI}_j\right)\ and the standard deviation \sigma\left({LLI}_j\right)\ are calculated.
STANDARDIZED ANOMALY COMPUTATION: Each month j and year k, the exceedance value is standardized according to the formula:
{LLI}_{std,j,k}=\frac{{LLI}_{j,k}-\mu\left(\ {EP}_j\right)}{\sigma\left(\ {EP}_j\right)}
vi) E3CI
For each month j and year k, the European Extreme Events Climate Index is given by the mean of the different components. Different and more effective formulations are currently under development.
